37 research outputs found
Orthosymplectic Yangians
We study the RTT orthosymplectic super Yangians and present their Drinfeld
realizations for any parity sequence, generalizing the results of for non-super
types BCD, a standard parity sequence, and super A-type.Comment: v1: 64pp, comments are welcome
Rational Lax matrices from antidominantly shifted extended Yangians: BCD types
Generalizing our recent joint paper with Vasily Pestun (arXiv:2001.04929), we
construct a family of rational Lax matrices,
polynomial in the spectral parameter, parametrized by the divisors on the
projective line with coefficients being dominant integral coweights of
associated Lie algebras. To this end, we provide the RTT realization of the
antidominantly shifted extended Drinfeld Yangians of , and of their coproduct
homomorphisms. This establishes some of the recent conjectures in the physics
literature by Costello-Gaiotto-Yagi (arXiv:2103.01835) in the classical types.Comment: v3: 67 pages, minor corrections, details added. v2: 65 pages, minor
corrections, some details added, Remark 4.37 added. v1: 64 pages, comments
are welcome
Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains
We continue our systematic construction of Baxter Q-operators for spin
chains, which is based on certain degenerate solutions of the Yang-Baxter
equation. Here we generalize our approach from the fundamental representation
of gl(n) to generic finite-dimensional representations in quantum space. The
results equally apply to non-compact representations of highest or lowest
weight type. We furthermore fill an apparent gap in the literature, and provide
the nearest-neighbor Hamiltonians of the spin chains in question for all cases
where the gl(n) representations are described by rectangular Young diagrams, as
well as for their infinite-dimensional generalizations. They take the form of
digamma functions depending on operator-valued shifted weights.Comment: 26 pages, 1 figur
Exact solution of an integrable non-equilibrium particle system
We consider the boundary-driven interacting particle systems introduced in
[FGK20a] related to the open non-compact Heisenberg model in one dimension. We
show that a finite chain of sites connected at its ends to two reservoirs
can be solved exactly, i.e. the non-equilibrium steady state has a closed-form
expression for each . The solution relies on probabilistic arguments and
techniques inspired by integrable systems. It is obtained in two steps: i) the
introduction of a dual absorbing process reducing the problem to a finite
number of particles; ii) the solution of the dual dynamics exploiting a
symmetry obtained from the Quantum Inverse Scattering Method. The exact
solution allows to prove by a direct computation that, in the thermodynamic
limit, the system approaches local equilibrium. A by-product of the solution is
the algebraic construction of a direct mapping (a conjugation) between the
generator of the non-equilibrium process and the generator of the associated
reversible equilibrium process.Comment: 46 pages, 2 figure
Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
In this note we construct Q-operators for the spin s open Heisenberg XXX
chain with diagonal boundaries in the framework of the quantum inverse
scattering method. Following the algebraic Bethe ansatz we diagonalise the
introduced Q-operators using the fundamental commutation relations. By acting
on Bethe off-shell states and explicitly evaluating the trace in the auxiliary
space we compute the eigenvalues of the Q-operators in terms of Bethe roots and
show that the unwanted terms vanish if the Bethe equations are satisfied.Comment: 17 page
Orthosymplectic superoscillator Lax matrices
We construct Lax matrices of superoscillator type that are solutions of the
RTT-relation for the rational orthosymplectic -matrix, generalizing
orthogonal and symplectic oscillator type Lax matrices previously constructed
by the authors in arXiv:2001.06825, arXiv:2104.14518 and arXiv:2112.12065. We
further establish factorisation formulas among the presented solutions.Comment: 25 page
Integrable heat conduction model
We consider a stochastic process of heat conduction where energy is
redistributed along a chain between nearest neighbor sites via an improper beta
distribution. Similar to the well-known Kipnis-Marchioro-Presutti (KMP) model,
the finite chain is coupled at its ends with two reservoirs that break the
conservation of energy when working at different temperatures. At variance with
KMP, the model considered here is integrable and one can write in a closed form
the -point correlation functions of the non-equilibrium steady state. As a
consequence of the exact solution one can directly prove that the system is in
a `local equilibrium' and described at the macro-scale by a product measure.
Integrability manifests itself through the description of the model via the
open Heisenberg chain with non-compact spins. The algebraic formulation of the
model allows to interpret its duality relation with a purely absorbing particle
system as a change of representation.Comment: 27 page
Bethe ansatz for Yangian invariants: Towards super YangâMills scattering amplitudes
We propose that Baxter's Z -invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies of an auxiliary inhomogeneous spin chain. As a consequence they are special solutions to the eigenvalue problem of the associated transfer matrix. Excitingly, this allows to construct them using Bethe ansatz techniques. Conceptually, our construction generalizes to general (super) Lie algebras and general representations. Here we present the explicit form of sample invariants for totally symmetric, finite-dimensional representations of gl(n) in terms of oscillator algebras. In particular, we discuss invariants of three- and four-site monodromies that can be understood respectively as intertwiners of the bootstrap and YangâBaxter equation. We state a set of functional relations significant for these representations of the Yangian and discuss their solutions in terms of Bethe roots. They arrange themselves into exact strings in the complex plane. In addition, it is shown that the sample invariants can be expressed analogously to GraĂmannian integrals. This aspect is closely related to a recent on-shell formulation of scattering amplitudes in planar N=4 super YangâMills theory
An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
We introduce a series of articles reviewing various aspects of integrable
models relevant to the AdS/CFT correspondence. Topics covered in these reviews
are: classical integrability, Yangian symmetry, factorized scattering, the
Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in
(conformal) quantum field theory. In the present article we highlight how these
concepts have found application in AdS/CFT, and provide a brief overview of the
material contained in this series.Comment: v2, published versio